Much of the earth's remaining natural gas and oil is located in rock shale and rock formations at depths varying from 500-20,000 feet below the surface. Many of the naturally occurring formations suffer from low porosity and permeability, thereby restricting natural gas and/or oil to flow into a well bore where the gas and/or oil can be recovered.
Hydraulic fracturing is a process that creates fractures in low porosity, low permeability rocks of geological formations. A hydraulic fracture may be formed by pumping a fracturing fluid mixture into a well bore at a rate sufficient to increase pressure down-hole to a value in excess of the fracture gradient of the formation rock. The pressure causes the formation to crack or fracture, which allows the fracturing mixture to enter and extend the crack further into the formation.
To keep a fracture open after the pumping process stops, the fracturing fluid mixture contains a solid, called a proppant, that remains in the new fracture and keeps the fracture open. Various types of proppant may be used depending on the permeability or grain strength needed. A completed fracture provides a conductive path connecting a large area of the reservoir to the well, thereby increasing the area from which oil, natural gas and liquids can be recovered from the targeted formation.
Propped hydraulic fracture stimulation is widely used to improve well productivity from tight, otherwise noncommercial reservoirs. Other areas of application include sand control in weakly consolidated reservoirs, gas condensate fields, and high permeability reservoirs that show significant permeability anisotropy.
An important consideration in the practice of hydraulic fracturing is “proppant flow-back”, i.e., the production of proppant back to the surface. Proppant flow-back can lead to damaged equipment and downtime, which necessitates costly and manpower intensive surface handling procedures. Proppant flow-back also presents a problem of proppant disposal. In some cases, a well can be prematurely abandoned if costs to return the well to production are excessive. Proppant flow-back, although not desirable, can be tolerated in certain operational environments. However, proppant flow-back from a fracture during the production phase is problematic. In practice, 20% to 50% of the original proppant pumped into a formation may be produced back.
An integral part of a hydraulic fracturing process is the introduction of proppant particles of various sizes into a fracture to hold the fractures open. Examples of proppants include structural materials such as sand, man-made ceramics, walnut shells and even polymer beads. Additionally, resin coated proppants have been used in an effort to reduce proppant flow-back. The resin coated proppant approach of gluing the sand together at the interface was an excellent starting point to reduce flow-back but mechanical cycling tends to crack the bonds that interconnect the proppant grains, thereby creating failure.
Studies have been undertaken to determine the mechanisms of flow-back. Laboratory work and theoretical simulations of several thousand individual proppant grains have shown that flow-back of plain proppant is critically dependent upon the ratio of mean grain diameter to fracture width. This dependence can be visualized as larger “columns” of proppants that have a greater tendency to buckle under loading. As a result of closure stress and inter-particle friction, a geometrically irregular arch of proppant grains is formed behind the fracture mouth. The buckled columns of proppant in front of the arch carry virtually no load. Therefore, small levels of proppant are initially transported to the well-bore even at low fluid flow rates. The loaded arch is stable until a sufficient fluid drag force is reached that is able to collapse the arch. A collapsing arch results in further proppant flow-back. An arch is a curved structure spanning an opening, serving to support a load by resolving the normal stress into lateral stress. For an arch to form, closure stress is required to generate a reaction force with the face of the fracture. The resolution of the forces in an arch necessarily sets up a pattern of shearing stresses within the material. At high closure stress these shear forces can become excessive and lead to pack failure.
Modes of proppant pack failure leading to proppant flow back are thought to be caused by arch destabilization due to excessive hydraulic and/or gravitational forces. Other modes of proppant pack failure are believed to include a fracture closure stress that is too low, proppant pack shear failure caused by too high fracture closure stress, as well as possible proppant crushing at high closure stress.
Critical parameters determining flow-back of plain proppants include fracture closure stress, both stabilizing and destabilizing. Other critical parameters include hydrodynamic force imposed from fluid production, which is destabilizing as the fluid flow tends to buckle proppant columns at the fracture mouth. Other critical parameters include the fracture width, which affects arch geometry and the transfer of friction and stress forces acting on proppants at a free face. Thus, for the same gradient, larger proppants will experience a greater destabilizing force. Similarly, at the fracture face the larger the proppant the fewer proppants per unit area are available to resist the applied closure stress and the larger the normal stress at the proppant contact.
A typical fracturing fluid mixture is made up of carrier fluid, additives and proppants. Typically, the carrier fluid and proppant comprise 99% of the mixture with less than 1% additives.
There are five types of carrier fluids normally used in the process. The five types are, 1) Water: which is typically un-gelled freshwater or formations of brine; 2) Cross-linked water-based fluids, which are gelled with polymers that employ a cross-linking agent, such as a metallic ion to bond the polymer molecules together for increasing fluid viscosity; 3) Oil-based fluids, which include gelled oils, diesel or lease crude; 4) Oil-in-water emulsions, which are external phase gelled water, internal phase gelled diesel, lease crude or condensates; and 5) Foam, which is a mixture of gas, e.g., nitrogen or carbon dioxide, gelled liquid, such as water or oils, and foaming agents, where mixtures are typically 60% to 80% gas.
Examples of typical additives used in the hydraulic fracturing industry include: acids; alcohols; bases; biocides; buffers; breakers; clay stabilizers and kcl substitutes; cross-linkers such as aluminum, boron, titanium, or zirconium; cross-link accelerators and delay agents; demulsifiers; foamers and defoamers, friction reducers; iron control agents; cellulose and guar polymers including standard, hpg, cmg, cmhpg; polymer slurries, including diesel and “green”; oxygen scavengers; salts; surfactants; and fluorosurfactants. This list of additives is only a representative portion of all additives used and is not meant to be a complete list.
Effectively dispersing a well-formulated fracturing fluid with a complex set of additives into a homogeneous emulsion is extremely difficult to accomplish due, primarily, because of chemical affinity mismatches that result from the broad diversity of the additives used. Additionally, because of the toxic nature of some of the chemicals used in hydraulic fracturing, industry is facing stiff and growing environmental regulation. Regulation is anticipated that will establish limits for various materials contained in hydraulic fracturing additives and carrier fluids.
Due to environmental issues associated with hydraulic fracturing, the oil and gas industry has shifted towards using water with mineral additives as the fracturing fluid of choice. The most commonly used additive in water hydraulic fracturing is a friction reducer.
Carrier fluids, additives and proppant must be mixed for use in hydraulic fracturing.
There are three types of commonly used mixing principles:
1. Static mixing, wherein liquids flow around fixed objects, either via force produced flow by pressure through mechanical means or gravity induced flow;
2. Dynamic mixing, wherein liquid induced mixing results from mechanical agitation via impellers, wiping blade and high shear turbines as well as single or double screw extruder designs or screw agitation designs; and
3. Kinetic mixing, wherein liquid is mixed by velocity impacts on a surface or wherein two or more liquids form a velocity impact by impinging on one another.
All three of the above mixing methods have one thing in common that hinders the optimizing of mixing regardless of the fluid being combined and regardless of whether the materials being mixed are polar, nonpolar, organic or inorganic etc. or if it is a filled material with compressible or non-compressible fillers.
The commonality that hinders optimizing of mixing is that all incompressible fluids have a wall effect or a boundary layer effect where the fluid velocity is greatly reduced at the wall or mechanical interface. Static mixing systems use this boundary layer to fold or blend the liquid using this resistive force to promote agitation.
Dynamic mixing, regardless of the geometry of mixing blades or turbine, results in dead zones and incomplete mixing because of the boundary layer. Dynamic mixing uses high shear and a screw blade designed to use the boundary layer to promote friction and compression by centrifugal forces to accomplish agitation while maintaining an incomplete mixed boundary layer on mechanical surfaces.
Kinetic mixing suffers from boundary layer effects on velocity profiles both on the incoming streams and at the injector tip. However, kinetic mixing suffers minimal boundary layer effects except for transport fluid phenomena.
A further explanation of the boundary layer of the flowing fluids follows. Aerodynamic forces depend in a complex way on the viscosity of a fluid. As a fluid moves past an object, the molecules in close proximity to the surface tend to stick to the surface. The molecules just above the surface are slowed down by their collisions with the molecules that are sticking to the surface. These molecules, in turn, slow down the flow just above them. The farther away from the surface, the fewer the collisions that are affected by the object surface. Therefore, a thin layer of fluid is created near the surface in which the velocity of the fluid changes from zero at the surface to the free stream value away from the surface. Engineers call this layer the “boundary layer” because the layer occurs on the boundary of the fluid.
As discussed above, as an object moves through a fluid, or as a fluid moves past an object, molecules of the fluid near the object are disturbed and as the molecules move around the object. Aerodynamic forces are generated between the fluid and the object. The magnitude of the aerodynamic forces depends on the shape of the object, the speed of the object, the mass of the fluid going by the object and on two other important properties of the fluid, i.e., the viscosity, or stickiness, and the compressibility, or springiness, of the fluid. To properly model these effects, aerospace engineers use similarity parameters, which are ratios of these effects to other forces present in the problem. If two experiments have the same values for the similarity parameters, then the relative importance of the forces are being correctly modeled.
Referring now to FIG. 1, a two dimensional representation of the streamwise velocity variation from free stream to the surface is shown. In reality, the effects are three dimensional. From the conservation of mass in three dimensions, a change in velocity in the streamwise direction causes a change in velocity in the other directions as well. A small component of velocity perpendicular to the surface displaces or moves the flow above it. The thickness of the boundary layer can be defined as the amount of this displacement. The displacement thickness depends on the Reynolds number, which is the ratio of inertial (resistant to change or motion) forces to viscous (heavy and gluey) forces and is given by the equation: Reynolds number (Re) equals velocity (V) times density (r) times a characteristic length (l) divided by the viscosity coefficient (mg), i.e., Re=V*r*l/mμ.
Still referring to FIG. 1, boundary layers may be either laminar (layered), or turbulent (disordered) depending on the value of the Reynolds number. For lower Reynolds numbers, the boundary layer is laminar and the streamwise velocity changes uniformly as a function of distance away from the wall, as may be seen on the left side of FIG. 1. For higher Reynolds numbers, the boundary layer is turbulent and the streamwise velocity is characterized by unsteady, or changing with time, swirling flows inside the boundary layer. The external flow reacts to the edge of the boundary layer just as it would to the physical surface of an object. Therefore, the boundary layer gives any object an effective shape, which is usually slightly different from the physical shape. The boundary layer may lift off or “separate” from the body and create an effective shape that is substantially different from the physical shape. Separation occurs because the flow in the boundary has very low energy relative to the free stream and is, therefore, more easily driven by changes in pressure. Flow separation is the reason for airplane wing stall at high angle of attack.
Boundary-Layer Flow
The portion of a fluid flow that occurs near a solid surface is where shear stresses are significant and is where inviscid-flow assumptions may not be used. Solid surfaces interact with a viscous fluid flow because of the no-slip condition discussed above, i.e., because of the physical requirement that fluid and solid have equal velocities at their interface. Therefore, fluid flow is retarded by a fixed solid surface, which results in the formation of a finite, slow-moving boundary layer. For the boundary layer to be thin, the Reynolds number of the body must be large, i.e., 103 or greater. Under these conditions the flow outside the boundary layer is essentially inviscid and plays the role of being a driving mechanism for the layer.
Referring now to FIG. 2, a typical low-speed or laminar boundary layer is shown. Such a display of the streamwise flow vector variation near a wall is called a velocity profile. The no-slip condition requires that u(x,0)=0, as shown, where u is the velocity of flow in the boundary layer. Velocity rises monotonically with distance y from the wall, finally merging smoothly with the outer (inviscid) stream velocity U(x). Assuming a Newtonian fluid, at any point in the boundary layer the fluid shear stress τ is proportional to the local velocity gradient. The value of the shear stress at the wall is most important, since the shear stress value relates not only to the drag of the body but often also to its heat transfer. At the edge of the boundary layer τ approaches zero asymptotically. There is no exact spot where τ=0, therefore the thickness δ of a boundary layer is usually defined arbitrarily as the point where u=0.99 U.
Friction Reducers
As stated above, additives in hydraulic fracturing fluid are typically deployed for use as friction reducers. As shown in FIG. 3, experiments were conducted wherein various friction reducers were added at a concentration of 0.25 gpt in 2% (wt) Kcl tap water flowing through a ½″ OD/0.402″ ID pipe. FIG. 4 shows experimental results comparing of 1.0 gpt of cationic friction reducers in several different fluids through a ½″ OD/0.402″ ID pipe. The graphs are discussed in SPE 119900, “Critical Evaluations of Additives Used in Shale Slickwater Fracs”; (P. Kaufman and G. S. Penny, CESI Chemical a Flotek Co. and J. Paktinat, Universal Well Services Inc.)
Each of FIGS. 3 and 4 show that there are two clear regions where the dispersion of a typical material is greatly influenced, i.e., at 0 to 10 seconds and again at 20 to 30 seconds. During the experiments, the fluid was recycled back into the loop through the circulation pump every 10 seconds. The circulation pump acted like a mixing system, thereby improving the material performance of the additive. The experimental results, represented by the curves of FIGS. 3 and 4, illustrate that dispersion of additives is crucial to the performance of the material. The periods of time from 0 to 10 second and from 20 to 30 seconds correlate to the times when typical friction reduction material passes through the mixing system in the cyclic loop process. The shape of the curves of FIGS. 3 and 4 indicate that, at about 10 seconds, the typical material has not been adequately dispersed and, therefore, is not distributed into the boundary layer of the flowing material. Therefore, the important disbursement of additives is desirable.